Mister Exam

# Sum of series f(xi)

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### The solution

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  oo
__
\
)   f*x*i
/_,
i = 1      
$$\sum_{i=1}^{\infty} f i x$$
Sum(f*(x*i), (i, 1, oo))
The radius of convergence of the power series
Given number:
$$f i x$$
It is a series of species
$$a_{i} \left(c x - x_{0}\right)^{d i}$$
- power series.
The radius of convergence of a power series can be calculated by the formula:
$$R^{d} = \frac{x_{0} + \lim_{i \to \infty} \left|{\frac{a_{i}}{a_{i + 1}}}\right|}{c}$$
In this case
$$a_{i} = f i x$$
and
$$x_{0} = 0$$
,
$$d = 0$$
,
$$c = 1$$
then
$$1 = \lim_{i \to \infty}\left(\frac{i}{i + 1}\right)$$
Let's take the limit
we find
True

False
oo*f*x
$$\infty f x$$
oo*f*x`